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Frequency Polygons

FoundationHigherAQAEdexcel

Revise Frequency Polygons for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. A frequency polygon joins the midpoints of the tops of the bars to show the shape of a distribution.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A frequency polygon shows the shape of a distribution using points joined by straight lines, and is particularly useful for comparing two distributions on the same axes.

Each point is plotted at the midpoint of its class interval, at a height equal to the frequency. The midpoint is found by adding the class boundaries and dividing by two.

Plotting at the midpoint is the detail most often got wrong — plotting at the start or end of the interval shifts the whole polygon sideways. The points are joined with straight lines and the polygon is not closed to the axis. Because two polygons can be drawn on the same axes, comparison is far easier than with two separate histograms.

Revision notes

Plotting the points

Each point is plotted at the midpoint of its class interval, at a height equal to the frequency.

Midpoint \(= \frac{\text{lower boundary} + \text{upper boundary}}{2}\). For the class \(10 \leq x < 20\) the midpoint is 15.

Drawing the polygon

Join consecutive points with straight lines.

The polygon is not closed down to the horizontal axis at either end. Both axes must be labelled.

Comparing distributions

Two frequency polygons can be drawn on the same axes, which makes comparison straightforward.

This is the main advantage over histograms, which become confusing when overlaid. Include a key to show which polygon is which.

Key points

  • Points are plotted at class midpoints.
  • The height is the frequency.
  • Midpoint = (lower + upper) ÷ 2.
  • Points are joined with straight lines.
  • The polygon is not closed to the axis.
  • Two polygons can be compared on one set of axes.

Worked examples

Example 1

A class is \(20 \leq x < 30\) with frequency 12. State the coordinates of the point to plot. [2 marks]

Working

Midpoint \(= \frac{20 + 30}{2} = 25\)work out the class midpoint
The point is \((25, 12)\)state the coordinates with the frequency as the height

Example 2

Explain why frequency polygons are useful for comparing two distributions. [2 marks]

Working

Both polygons can be drawn on the same pair of axesstate the property
so the shapes and positions of the two distributions can be compared directlyexplain the benefit

Example 3

A student plots points at the start of each class interval. Explain the error. [2 marks]

Working

Points must be plotted at the midpoint of each class intervalstate the correct method
so the whole polygon is shifted sideways and misrepresents the distributionexplain the effect

Common mistakes

  • Plotting at the start or end of the interval.

    Points must be at the midpoint.

  • Closing the polygon to the axis.

    It is left open at both ends.

  • Forgetting a key when comparing two polygons.

    The reader must be able to tell them apart.

  • Using the class width as the height.

    The height is the frequency.

Exam tips

  • Calculate each midpoint before plotting.
  • Join points with straight lines and leave the ends open.
  • Add a key when drawing two polygons.
  • Give coordinates as (midpoint, frequency).

Key terms

Frequency polygon
A diagram of class midpoints joined by straight lines.
Midpoint
The middle value of a class interval.
Distribution
The pattern of how data values are spread.
Class boundary
The upper or lower limit of a class interval.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.